Lack-of--t Detection Using the Run-distribution Test Lack-of--t Detection Using the Run-distribution Test

In this paper, we are concerned with the problem of deciding whether a tted model accurately describes the data to which it has been tted. We have developed an eeective method of testing the lack-of-t of a parametric model to data, with applications to the computer vision problems of robust estimation, model selection, and curve and surface segmentation. The beneets of this technique are high sensitivity (large response to small outliers) and very low dependence on the noise distribution of the input data. Our test is new to the computer vision community in several ways: We look at the distribution of the residual errors, rather than basing statistics directly on their values. We assume a broad enough class of distributions as to be essentially distribution independent. The test requires no knowledge of the sensor noise level, and its response is essentially independent of that level. We present results of experiments that compare the test with the standard 2 statistic, and the median absolute deviation (MAD) measure used in robust estimation. The experiments are designed to represent typical vision tasks, namely feature tracking, robust tting, and segmentation. We show that our test is comparable to the MAD and chi-square, but is cheaper than the MAD, and requires no knowledge of the noise level. Abstract In this paper, we are concerned with the problem of deciding whether a tted model accurately describes the data to which it has been tted. We have developed an eeective method of testing the lack-of-t of a parametric model to data, with applications to the computer vision problems of robust estimation, model selection, and curve and surface segmentation. The beneets of this technique are high sensitivity (large response to small outliers) and very low dependence on the noise distribution of the input data. Our test is new to the computer vision community in several ways: We look at the distribution of the residual errors, rather than basing statistics directly on their values. We assume a broad enough class of distributions as to be essentially distribution independent. The test requires no knowledge of the sensor noise level, and its response is essentially independent of that level. We present results of experiments that compare the test with the standard 2 statistic, and the median absolute deviation (MAD) measure used in robust estimation. The experiments are designed to represent typical vision tasks, namely feature tracking, robust tting, and segmentation. We …